Properties

Label 2550.2.a
Level $2550$
Weight $2$
Character orbit 2550.a
Rep. character $\chi_{2550}(1,\cdot)$
Character field $\Q$
Dimension $52$
Newform subspaces $41$
Sturm bound $1080$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2550.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 41 \)
Sturm bound: \(1080\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2550))\).

Total New Old
Modular forms 564 52 512
Cusp forms 517 52 465
Eisenstein series 47 0 47

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(5\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(4\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(21\)
Minus space\(-\)\(31\)

Trace form

\( 52q + 2q^{3} + 52q^{4} - 2q^{6} + 52q^{9} + O(q^{10}) \) \( 52q + 2q^{3} + 52q^{4} - 2q^{6} + 52q^{9} - 8q^{11} + 2q^{12} - 8q^{14} + 52q^{16} + 8q^{19} + 20q^{21} - 8q^{23} - 2q^{24} + 2q^{27} - 16q^{29} + 24q^{31} - 8q^{33} - 4q^{34} + 52q^{36} - 8q^{37} + 8q^{38} + 28q^{39} - 16q^{41} - 4q^{42} - 8q^{43} - 8q^{44} - 8q^{46} - 16q^{47} + 2q^{48} + 76q^{49} - 2q^{51} - 16q^{53} - 2q^{54} - 8q^{56} + 16q^{57} + 16q^{58} - 40q^{59} + 8q^{61} - 24q^{62} + 52q^{64} + 8q^{66} + 32q^{67} + 4q^{69} + 8q^{71} + 32q^{73} + 16q^{74} + 8q^{76} + 4q^{78} + 8q^{79} + 52q^{81} + 24q^{82} + 24q^{83} + 20q^{84} + 8q^{87} + 48q^{91} - 8q^{92} + 36q^{93} - 2q^{96} + 40q^{98} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2550))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5 17
2550.2.a.a \(1\) \(20.362\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-3\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-3q^{7}-q^{8}+\cdots\)
2550.2.a.b \(1\) \(20.362\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
2550.2.a.c \(1\) \(20.362\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
2550.2.a.d \(1\) \(20.362\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
2550.2.a.e \(1\) \(20.362\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
2550.2.a.f \(1\) \(20.362\) \(\Q\) None \(-1\) \(-1\) \(0\) \(3\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+3q^{7}-q^{8}+\cdots\)
2550.2.a.g \(1\) \(20.362\) \(\Q\) None \(-1\) \(-1\) \(0\) \(5\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+5q^{7}-q^{8}+\cdots\)
2550.2.a.h \(1\) \(20.362\) \(\Q\) None \(-1\) \(1\) \(0\) \(-3\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots\)
2550.2.a.i \(1\) \(20.362\) \(\Q\) None \(-1\) \(1\) \(0\) \(-2\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots\)
2550.2.a.j \(1\) \(20.362\) \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
2550.2.a.k \(1\) \(20.362\) \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
2550.2.a.l \(1\) \(20.362\) \(\Q\) None \(-1\) \(1\) \(0\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
2550.2.a.m \(1\) \(20.362\) \(\Q\) None \(-1\) \(1\) \(0\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
2550.2.a.n \(1\) \(20.362\) \(\Q\) None \(-1\) \(1\) \(0\) \(4\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots\)
2550.2.a.o \(1\) \(20.362\) \(\Q\) None \(-1\) \(1\) \(0\) \(4\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots\)
2550.2.a.p \(1\) \(20.362\) \(\Q\) None \(-1\) \(1\) \(0\) \(4\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots\)
2550.2.a.q \(1\) \(20.362\) \(\Q\) None \(-1\) \(1\) \(0\) \(4\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots\)
2550.2.a.r \(1\) \(20.362\) \(\Q\) None \(1\) \(-1\) \(0\) \(-4\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
2550.2.a.s \(1\) \(20.362\) \(\Q\) None \(1\) \(-1\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
2550.2.a.t \(1\) \(20.362\) \(\Q\) None \(1\) \(-1\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
2550.2.a.u \(1\) \(20.362\) \(\Q\) None \(1\) \(-1\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
2550.2.a.v \(1\) \(20.362\) \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
2550.2.a.w \(1\) \(20.362\) \(\Q\) None \(1\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
2550.2.a.x \(1\) \(20.362\) \(\Q\) None \(1\) \(-1\) \(0\) \(1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
2550.2.a.y \(1\) \(20.362\) \(\Q\) None \(1\) \(-1\) \(0\) \(2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots\)
2550.2.a.z \(1\) \(20.362\) \(\Q\) None \(1\) \(-1\) \(0\) \(3\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+3q^{7}+q^{8}+\cdots\)
2550.2.a.ba \(1\) \(20.362\) \(\Q\) None \(1\) \(1\) \(0\) \(-5\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-5q^{7}+q^{8}+\cdots\)
2550.2.a.bb \(1\) \(20.362\) \(\Q\) None \(1\) \(1\) \(0\) \(-3\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots\)
2550.2.a.bc \(1\) \(20.362\) \(\Q\) None \(1\) \(1\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
2550.2.a.bd \(1\) \(20.362\) \(\Q\) None \(1\) \(1\) \(0\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
2550.2.a.be \(1\) \(20.362\) \(\Q\) None \(1\) \(1\) \(0\) \(2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
2550.2.a.bf \(1\) \(20.362\) \(\Q\) None \(1\) \(1\) \(0\) \(3\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots\)
2550.2.a.bg \(2\) \(20.362\) \(\Q(\sqrt{33}) \) None \(-2\) \(-2\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-\beta q^{7}-q^{8}+\cdots\)
2550.2.a.bh \(2\) \(20.362\) \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(0\) \(-2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+(-1-\beta )q^{7}+\cdots\)
2550.2.a.bi \(2\) \(20.362\) \(\Q(\sqrt{6}) \) None \(-2\) \(2\) \(0\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+\beta q^{7}-q^{8}+\cdots\)
2550.2.a.bj \(2\) \(20.362\) \(\Q(\sqrt{6}) \) None \(2\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+\beta q^{7}+q^{8}+\cdots\)
2550.2.a.bk \(2\) \(20.362\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(0\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+(1+\beta )q^{7}+\cdots\)
2550.2.a.bl \(2\) \(20.362\) \(\Q(\sqrt{6}) \) None \(2\) \(2\) \(0\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+\beta q^{7}+q^{8}+\cdots\)
2550.2.a.bm \(2\) \(20.362\) \(\Q(\sqrt{33}) \) None \(2\) \(2\) \(0\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+\beta q^{7}+q^{8}+\cdots\)
2550.2.a.bn \(3\) \(20.362\) 3.3.568.1 None \(-3\) \(-3\) \(0\) \(-6\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+(-2-\beta _{1}+\cdots)q^{7}+\cdots\)
2550.2.a.bo \(3\) \(20.362\) 3.3.568.1 None \(3\) \(3\) \(0\) \(6\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+(2+\beta _{1})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2550))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2550)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(255))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(425))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(510))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(850))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1275))\)\(^{\oplus 2}\)